If B = [[1, 0, 2], [0, 1, 3], [0, 0, 1]], what is the rank of matrix B?

If B = [[1, 0, 2], [0, 1, 3], [0, 0, 1]], what is the rank of matrix B?

Step 1: Write down the matrix B: [[1, 0, 2], [0, 1, 3], [0, 0, 1]].
Step 2: Identify the rows of the matrix. There are 3 rows: [1, 0, 2], [0, 1, 3], and [0, 0, 1].
Step 3: Check each row to see if it is a non-zero row. A non-zero row is a row that has at least one number that is not zero.
Step 4: The first row [1, 0, 2] is non-zero because it has '1' and '2'.
Step 5: The second row [0, 1, 3] is also non-zero because it has '1' and '3'.
Step 6: The third row [0, 0, 1] is non-zero because it has '1'.
Step 7: Count the number of non-zero rows. There are 3 non-zero rows.
Step 8: The rank of matrix B is equal to the number of non-zero rows, which is 3.

Matrix Rank – The rank of a matrix is the dimension of the vector space generated by its rows or columns, which can be determined by the number of non-zero rows in its row echelon form.
Row Echelon Form – A matrix is in row echelon form if all non-zero rows are above any rows of all zeros, and the leading coefficient of a non-zero row is always to the right of the leading coefficient of the previous row.